The sum of the digits of two digit number is 14 and the difference between the two digits of the number is 2. What is the product of the two digits of the two digit number?

Options

A. 56
B. 48
C. 45
D. Couldn/t be determined

Answer

To solve the problem step by step, we will denote the two digits of the two-digit number as \( x \) (the tens digit) and \( y \) (the units digit).

### Step 1: Set up the equations based on the problem statement.
We know from the problem that:
1. The sum of the digits is 14:
\[ x + y = 14 \]
2. The difference between the two digits is 2:
\[ x - y = 2 \]

### Step 2: Solve the equations simultaneously.
We can solve these two equations together.

First, we can add the two equations:
\[ (x + y) + (x - y) = 14 + 2 \]
This simplifies to:
\[ 2x = 16 \]
Now, divide both sides by 2:
\[ x = 8 \]

### Step 3: Substitute the value of \( x \) back into one of the equations to find \( y \).
Now that we have \( x \), we can substitute it back into the first equation:
\[ 8 + y = 14 \]
Subtract 8 from both sides:
\[ y = 14 - 8 = 6 \]

### Step 4: Calculate the product of the two digits.
Now that we have both digits, \( x = 8 \) and \( y = 6 \), we can find the product:
\[ x \cdot y = 8 \cdot 6 = 48 \]

### Final Answer:
The product of the two digits of the two-digit number is \( 48 \).

---